Sweet Trims are made of Threes: A c\`adl\`ag erasure of the Brownian tree

TL;DR

The paper introduces a trimming algorithm for binary trees that produces a cdle0g erasure of Brownian trees, linking combinatorial tree processes with continuous stochastic limits.

Contribution

It presents a novel simple trimming procedure that connects discrete binary trees with their continuous Brownian tree limits through a cdle0g erasure.

Findings

The trimming algorithm generates nested binary trees via leaf removal.

Its scaling limit yields a cdle0g erasure of Brownian trees.

The process relates to SLE theory and known coupling methods.

Abstract

We present a simple trimming algorithm that generates nested uniform binary plane trees by removing leaves one-by-one using a best-of-three-match procedure. While its one-step transition specializes to the Luczak-Winkler & Caraceni-Stauffer coupling, its scaling limit provides a suprising c\`adl\`ag erasure of Brownian trees, reminiscent of SLE theory.